(Quick aside here. This is the only time when the third-person narrator describes plot having directly to do with Esther. But even though she quickly is addressed by Jarndyce in this chapter, she is never actually seen until the narration switches back to her voice in Chapter 57. All of which is to say – we've got kind of a Clark Kent/Superman thing going on here with them.)
Volumnia finds Sir Dedlock on the floor of the study.
He's had a fit, can barely speak, and is communicating by writing on a piece of paper. Mrs. Rouncewell is taking care of him.
He asks for Lady Dedlock, who can't be found, and is given her letter.
He cries and moans after reading it, then asks for Bucket.
He lets Bucket read the letter, then writes on his chalkboard, "Full forgiveness. Find---" (56.20).
Bucket first tells Mrs. Rouncewell to take care of Sir Dedlock and not to worry about her son, because George has already been released.
Then Bucket immediately takes off. First looking for some clues in Lady Dedlock's room, he finds Esther Summerson's handkerchief – and hey, what a good thing all handkerchiefs back then were monogrammed! Her name is written right on it.
Bucket immediately remembers her from Gridley's deathbed and puts two and two together.
He rides off to George Rouncewell's and gets Jarndyce's address.
At Jarndyce's he asks to take Esther with him as they search for Lady Dedlock. His idea is that if she sees the two of them together, she'll be more likely to believe him when he says that Sir Dedlock has already forgiven her for everything.